The distance from Earth to the sun is 1.5×10⁸ km. Find the number of crests in a light wave of frequency 1.0×10¹⁴ s ^–1 traveling from the sun to Earth.

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Welcome back Everyone in this example, we're told that at its farthest distance the Earth to the sun would be 1.52 times 10 to the 10th power kilometers were told that if UV light from the sun has a frequency of three point oh times 10th of 16 power hurts to calculate the number of crests for the wave. So we want to recall that frequency is represented by this symbol and it can be in units of hertz which are equivalent to inverse seconds. And because the prompt is asking us to calculate number of crests, this is in reference to our wavelength. So recall that wavelength is represented by the symbol lambda. And when we imagine our wave of our UV light, we would recognize that our crests and let's make that meter. So our crests are going to be these peaks here. So this is a crust of our wavelength. So what we want to recall is how to calculate wavelength. And we would recall the formula where frequency is equal to our speed of light divided by lambda wavelength and so two sulfur wavelength. We would say that that is equal to the speed of light divided by our frequency. So we can go ahead and plug in what we know. And in our numerator we would recall that the speed of light is a constant value of 3. times 10 to the eighth power meters per second. Whereas in our denominator we're going to plug in that frequency given in the prompt and we'll use the color purple here. So it's given as 3.2 times 10 to the 16th power However, because we need to cancel out our units of seconds. We're going to utilize inverse second units, which we understand are equal to hurts as we stated earlier. So this allows us to get rid of our units of seconds with inverse seconds. Leaving us with meters as our unit for wavelength, which is fine. And what we're going to get here is a value for our quotient equal to our wavelength of 1.0 times 10 to the negative eighth power meters. And this is going to be our wavelength for our U. V light. So moving on, we will go ahead and utilize the distance given in the prompt as 1.52 times 10 to the 10th power kilometers. But because we just calculated wavelength in meters, we want to get rid of that unit kilometers. So we're going to recall to convert from kilometers two m by recognizing that our prefix kilo tells us that we have 10 to the third power kilometers or meters for one kilometer. This allows us to cancel out kilometers and now we're left with meters where we can incorporate our calculation from above, which is our wavelength by recalling that we have 1.0 times 10 to the negative eighth power meters for our wave of UV light and this is for one wave of UV light. And so this allows us to now get rid of our units of meters, we're left with units of waves here. So for our final result, we're going to get a value that is equal to 1. times 10 to the 21st power waves. And this would be our final result because we understand that frequency, or sorry, wavelength is measured from crest to crest as we shown above. And so our number of crests we would say, is therefore going to be 1.52 times 10 to the 21st power plus one. This will be our total number of crusts. And so it would be this quantity here. That would be our final answer to complete this example. So I hope that everything that I explained was clear. If you have any questions, please lead them down below and I will see everyone in the next practice video.

The distance from Earth to the sun is 1.5×10⁸ km. Find the number of crests in a light wave of frequency 1.0×10¹⁴ s ^–1 traveling from the sun to Earth.

Verified Solution

Key Concepts

Wave Properties

Speed of Light

Calculating Wave Crests

The distance from Earth to the sun is 1.5×108 km. Find the number of crests in a light wave of frequency 1.0×1014 s –1 traveling from the sun to Earth.

Verified Solution

Key Concepts

Wave Properties

Speed of Light

Calculating Wave Crests

The distance from Earth to the sun is 1.5×10⁸ km. Find the number of crests in a light wave of frequency 1.0×10¹⁴ s ^–1 traveling from the sun to Earth.